{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 知识点梳理\n",
    "1. 相关概念（生成模型、判别模型)\n",
    "2. 先验概率、条件概率\n",
    "3. 贝叶斯决策理论\n",
    "4. 贝叶斯定理公式\n",
    "5. 极值问题情况下的每个类的分类概率\n",
    "6. 下溢问题如何解决\n",
    "7. 零概率问题如何解决？\n",
    "8. 优缺点\n",
    "9. sklearn参数详解，Python绘制决策树\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sklearn接口"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier Score: 0.9666666666666667\n"
     ]
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.datasets import load_iris\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "iris = load_iris()\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.2)\n",
    "clf = GaussianNB().fit(X_train, y_train)\n",
    "print (\"Classifier Score:\", clf.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table>\n",
    "<thead>\n",
    "<tr>\n",
    "  <th align=\"center\">编号</th>\n",
    "  <th align=\"center\">色泽</th>\n",
    "  <th align=\"center\">根蒂</th>\n",
    "  <th align=\"center\">敲声</th>\n",
    "  <th align=\"center\">纹理</th>\n",
    "  <th align=\"center\">脐部</th>\n",
    "  <th align=\"center\">触感</th>\n",
    "  <th align=\"center\">好瓜</th>\n",
    "</tr>\n",
    "</thead>\n",
    "<tbody><tr>\n",
    "  <td align=\"center\">1</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">2</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">沉闷</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">3</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">4</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">沉闷</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">5</td>\n",
    "  <td align=\"center\">浅白</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">6</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">软粘</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">7</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">稍糊</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">软粘</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">8</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">是</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">9</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">沉闷</td>\n",
    "  <td align=\"center\">稍糊</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">10</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">硬挺</td>\n",
    "  <td align=\"center\">清脆</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">平坦</td>\n",
    "  <td align=\"center\">软粘</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">11</td>\n",
    "  <td align=\"center\">浅白</td>\n",
    "  <td align=\"center\">硬挺</td>\n",
    "  <td align=\"center\">清脆</td>\n",
    "  <td align=\"center\">模糊</td>\n",
    "  <td align=\"center\">平坦</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">12</td>\n",
    "  <td align=\"center\">浅白</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">模糊</td>\n",
    "  <td align=\"center\">平坦</td>\n",
    "  <td align=\"center\">软粘</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">13</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">稍糊</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">14</td>\n",
    "  <td align=\"center\">浅白</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">沉闷</td>\n",
    "  <td align=\"center\">稍糊</td>\n",
    "  <td align=\"center\">凹陷</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">15</td>\n",
    "  <td align=\"center\">乌黑</td>\n",
    "  <td align=\"center\">稍蜷</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">清晰</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">软粘</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">16</td>\n",
    "  <td align=\"center\">浅白</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">浊响</td>\n",
    "  <td align=\"center\">模糊</td>\n",
    "  <td align=\"center\">平坦</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "<tr>\n",
    "  <td align=\"center\">17</td>\n",
    "  <td align=\"center\">青绿</td>\n",
    "  <td align=\"center\">蜷缩</td>\n",
    "  <td align=\"center\">沉闷</td>\n",
    "  <td align=\"center\">稍糊</td>\n",
    "  <td align=\"center\">稍凹</td>\n",
    "  <td align=\"center\">硬滑</td>\n",
    "  <td align=\"center\">否</td>\n",
    "</tr>\n",
    "</tbody></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 1. 相关概念\n",
    "\n",
    "生成模型：在概率统计理论中, 生成模型是指能够随机生成观测数据的模型，尤其是在给定某些隐含参数的条件下。它给观测值和标注数据序列指定一个联合概率分布。在机器学习中，生成模型可以用来直接对数据建模（例如根据某个变量的概率密度函数进行数据采样），也可以用来建立变量间的条件概率分布。条件概率分布可以由生成模型根据贝叶斯定理形成。常见的基于生成模型算法有高斯混合模型和其他混合模型、隐马尔可夫模型、随机上下文无关文法、朴素贝叶斯分类器、AODE分类器、潜在狄利克雷分配模型、受限玻尔兹曼机  \n",
    "<br>\n",
    "举例：要确定一个瓜是好瓜还是坏瓜，用判别模型的方法是从历史数据中学习到模型，然后通过提取这个瓜的特征来预测出这只瓜是好瓜的概率，是坏瓜的概率。\n",
    "\n",
    "<br>\n",
    "判别模型: 在机器学习领域判别模型是一种对未知数据 y 与已知数据 x 之间关系进行建模的方法。判别模型是一种基于概率理论的方法。已知输入变量 x ，判别模型通过构建条件概率分布 P(y|x) 预测 y 。常见的基于判别模型算法有逻辑回归、线性回归、支持向量机、提升方法、条件随机场、人工神经网络、随机森林、感知器\n",
    "\n",
    "举例：利用生成模型是根据好瓜的特征首先学习出一个好瓜的模型，然后根据坏瓜的特征学习得到一个坏瓜的模型，然后从需要预测的瓜中提取特征，放到生成好的好瓜的模型中看概率是多少，在放到生产的坏瓜模型中看概率是多少，哪个概率大就预测其为哪个。\n",
    "\n",
    "<br>\n",
    "生成模型是所有变量的全概率模型，而判别模型是在给定观测变量值前提下目标变量条件概率模型。因此生成模型能够用于模拟（即生成）模型中任意变量的分布情况，而判别模型只能根据观测变量得到目标变量的采样。判别模型不对观测变量的分布建模，因此它不能够表达观测变量与目标变量之间更复杂的关系。因此，生成模型更适用于无监督的任务，如分类和聚类。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 先验概率、条件概率\n",
    "条件概率: 就是事件A在事件B发生的条件下发生的概率。条件概率表示为P（A|B），读作“A在B发生的条件下发生的概率”。\n",
    "\n",
    "<br>\n",
    "先验概率: 在贝叶斯统计中，某一不确定量 p 的先验概率分布是在考虑\"观测数据\"前，能表达 p 不确定性的概率分布。它旨在描述这个不确定量的不确定程度，而不是这个不确定量的随机性。这个不确定量可以是一个参数，或者是一个隐含变量。\n",
    "\n",
    "<br>\n",
    "后验概率: 在贝叶斯统计中，一个随机事件或者一个不确定事件的后验概率是在考虑和给出相关证据或数据后所得到的条件概率。同样，后验概率分布是一个未知量（视为随机变量）基于试验和调查后得到的概率分布。“后验”在本文中代表考虑了被测试事件的相关证据。\n",
    "<br>\n",
    "\n",
    "通过上述西瓜的数据集来看\n",
    "\n",
    "条件概率，就是在条件为瓜的颜色是青绿的情况下，瓜是好瓜的概率\n",
    "\n",
    "先验概率，就是常识、经验、统计学所透露出的“因”的概率，即瓜的颜色是青绿的概率。\n",
    "\n",
    "后验概率，就是在知道“果”之后，去推测“因”的概率，也就是说，如果已经知道瓜是好瓜，那么瓜的颜色是青绿的概率是多少。后验和先验的关系就需要运用贝叶斯决策理论来求解。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 贝叶斯决策理论\n",
    "贝叶斯决策论是概率框架下实施决策的基本方法，对分类任务来说，在所有相关概率都已知的理想情形下，贝叶斯决策论考虑如何基于这些概率和误判损失来选择最优的类别标记。\n",
    "\n",
    "假设有N种可能标记， $λ_{ij}$是将类$c_j$误分类为$c_i$所产生的损失，基于后验概率$ P(c_i | x)$ 可以获得样本x分类为$c_i$所产生的期望损失 ，即在样本x上的条件风险：\n",
    "\n",
    "$$R(c_i|\\mathbf{x}) = \\sum_{j=1}^N \\lambda_{ij} P(c_j|\\mathbf{x})$$\n",
    "我们的任务是寻找一个判定准则 $h:X→Y$以最小化总体风险\n",
    "\n",
    "$$R(h)= \\mathbb{E}_x [R(h(\\mathbf(x)) | \\mathbf(x))]$$\n",
    "\n",
    "显然，对每个样本x，若h能最小化条件风险 $R(h((x))|(x))$,则总体风险R(h)也将被最小化。这就产生了贝叶斯判定准则：为最小化总体风险，只需要在每个样本上选择那个能使条件风险R(c|x)最小的类别标记，即：\n",
    "\n",
    "$$h^* (x) = argmin_{c\\in y} R(c|\\mathbf{x})$$\n",
    "此时，h 称作贝叶斯最优分类器，与之对应的总体风险R(h )称为贝叶斯风险，1-R(h*)反映了分类器能达到的最好性能，即机器学习所产生的模型精度的上限。\n",
    "\n",
    "具体来说，若目标是最小化分类错误率（对应0/1损失），则$λ_{ij}$可以用0/1损失改写，得到条件风险和最小化分类错误率的最优分类器分别为：\n",
    "$$R(c|\\mathbf{x}) = 1- P(c|\\mathbf{x})$$\n",
    "\n",
    "$$h^*(x) = argmax_{c\\in \\mathcal{Y}} P(c|\\mathbf{x})$$\n",
    "\n",
    "即对每个样本x，选择能使后验概率P(c|x)最大的类别标识。\n",
    "\n",
    "获得后验概率的两种方法：\n",
    "\n",
    "1. 判别式模型:给定x，可以通过直接建模P(c|x)来预测c。\n",
    "2. 生成模型:先对联合分布p(x, c)建模，然后再有此获得P(c|x)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 贝叶斯公式\n",
    "对生成模型来说，必然考虑：\n",
    "$$P(c|x) = \\frac{P(x,c)}{P(x)} = \\frac{P(c) P(x|c)}{P(x)}$$\n",
    "其中P(c)是“先验概率”；\n",
    "\n",
    "P(x|c)是样本x对于类标记c的类条件概率，或称为“似然”；\n",
    "\n",
    "P(x)是用于归一化的“证据”因子。\n",
    "\n",
    "上式即为贝叶斯公式。\n",
    "\n",
    "可以将其看做$$P(类别|特征) = \\frac{P(特征,类别)}{P(特征)} = \\frac{P(类别) P(特征|类别)}{P(特征)}$$\n",
    "\n",
    "对类条件概率P(x|c)来说，直接根据样本出现的频率来估计将会遇到严重的困难，所以引入了极大似然估计。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 极大似然估计\n",
    "估计类条件概率有一种常用的策略就是先假定其具有某种确定的概率分布形式，再基于训练样本对概率分布的参数进行估计。假设P(x|c)具有某种确定的形式并且被参数$θ_c$ 唯一确定，则我们的任务就是利用训练结D估计参数 $θ_c$。为了明确期间，我们将P(x|c)记为$p(x|θc)$.\n",
    "\n",
    "举个通俗的例子：假设一个袋子装有白球与红球，比例未知，现在抽取10次（每次抽完都放回，保证事件独立性），假设抽到了7次白球和3次红球，在此数据样本条件下，可以采用最大似然估计法求解袋子中白球的比例（最大似然估计是一种“模型已定，参数未知”的方法）。当然，这种数据情况下很明显，白球的比例是70%，但如何通过理论的方法得到这个答案呢？一些复杂的条件下，是很难通过直观的方式获得答案的，这时候理论分析就尤为重要了，这也是学者们为何要提出最大似然估计的原因。我们可以定义从袋子中抽取白球和红球的概率如下：\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "x1为第一次采样，x2为第二次采样，f为模型, theta为模型参数"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中$\\theta$是未知的，因此，我们定义似然L为：\n",
    "![image.png](attachment:image.png)\n",
    "L为似然的符号"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "两边取ln，取ln是为了将右边的乘号变为加号，方便求导。\n",
    "![image.png](attachment:image.png)\n",
    "两边取ln的结果，左边的通常称之为对数似然。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)这是平均对数似然"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最大似然估计的过程，就是找一个合适的theta，使得平均对数似然的值为最大。因此，可以得到以下公式：\n",
    "![image.png](attachment:image.png)最大似然估计的公式"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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Tm4Azz78YWb4gevTpi6TEWKQkJiE5rS7GvjRFyB4sykOxLwcL5kxF7QZ10KVfX2zN9SK3KIDbbr8FCfEenHB8U3Tr3gVdevXF1d164d4H/y0d1dm+CSy0lOKapev69kK8x4OElGpIr380tub68O0PP+G4Fs2QmpiAOE+MqEW5NoOGHZyHo+XUgw8Okbk4T2wckpM5Z+BBjZRkfP71N9IGaLrIUfrXX38t6zKOOuooPP3009IpuJFkSgrn6Dx44vGnwH1PKQ2xIy1cNB9dunYUCypPjEfi1KtfB59++qnN8EaNGmWfgnrOOefIM36faZ/OLzXXYRZdDBTswNC7b0ZcQhJeGPeqRGCnePDhoZg5b76dWCcnN21cjZS0VJlPvG/oSJHXbVmKGWuXUB/AE489LuVOS07DhHGvoDCfhi9WWRzAQnBpdfop0kGrV6+OdesMONuFiHJRFXCZ/sY0HN+8BRLiYqQ8pHevvjfhl19XCevYunENbhg4QJ4lJibKBp9lM+8wFaMUq8pBBJfXXnkFJx17PFKSEkz54mLQoVNf/PAjNxINIXP7Rrt8KSkpYgZbdvmqXISDIkEkuPA8Ih7QyLrkr2/fvvjttz+kHW7cuBEDb6AWyYPEhFTcfts9+GsF67rqgwXWtvlZ9a7gUlQEBAuBws1odcKR0na79u4nA1nytXA6oBS48DGZTmx8IuITU9G1S28UekMo8lkvkd6kUosX48aMQI3UeMTGVcMD/xlugQvlbuqUD/29xfwBoy7K3r4GtTIS4Ymthq+/WyEjjYAvGyjKxl3/d7NUeEpGHfzw+wphUFSZPfnovzH03tuREseGEo+jmp2I/z45Eg88PAzX/au/1YDi8eyocbL7NEJefPnhO6ieEocmzVtITWz3GiUkReP+fbtLmrj4GIx4fhQmzZqHd97/yGzNY6mNOHlNR+nlkUcewaiRwyUNwSW+Wi0s+3M1jjqmBe6+czDmz5opiwSPrHekVRYPFr31Lm659Q6cfdY/8cKLYzF12izcdtttSIuNQfXEeDQ99gRkew37/Wv5CpBp8tRSHi7HEbWqc+74v8H29/3y8/ISHcDrzcXgu24FwYVrQFq3PkO2m9DdIrZv3y7ns1Bi0jyZQVmqMW25Bgm8OKlxXSSnpiErPwCvH1j990a0bXe5SCXZtOtnR7LAat7caYiJZ/0k4tVZ74qsbitrmLEVV+ZSigFvfgGOanCkqMRqpGXAm1eEnEwzz8O5GKfUQnBJTIwXOhx//PElLTFNEUr9lwUupSJaAd6sLHuhsyc5FU/97xW7yEX5OzBuzGh5P02rVQ0YPa8wFaM/37XQwuxsnNbyBClDTEoaHhr2LAptAvvw0tgX5WA3frfrIP3gpJNOEnolJiTj+edH22QpKMjGmHEj4Yn1YOaMuShUzZgdo/IXrG3zs+pdwSXI+UKfgEuPDhehWjUOvOKwLTtPFPbhdIBHb8xrTUYDBw6UwickVcc9dz+ESa9Px/RpszF92kxMmToJs2ZPxdRpL2PBgjdwRqsWSIw1KPrxFz+EwUWAZf+Dy8iRI9GjRw9ZYXr11VejY8eOVfo988wzQprydL4cdT/56P1ISfSIBJfFaRZxHBMX4pP3FyG1Wg2h6cjRE6QSZE6DlRTIw3mtTkFCUhqq12mI62+705qbKcbIp0Zg4KBB2JZF1RUB24szT2qBlLg4DLzpdnkDlUpk5Ry1f/vV5/IOjlweGvao1IXVNKzyRPFCPlze5kLExqUiJjkDV3frg61Z+WbthqzqAxbMm2/ne2TDJrjl1sEo8hcjN68QefkB+Av9ApKUgGISqmPpzytRkJeHR4c+LOlq1EgH1WmkEx3L+sUXX8iz2JhkPDPyBcdENmMwXgCXtbvIfu9LL70k4EEGyDq86qqrRPXDvFRiUT/KV1pBxcha9ycy4j04o/XZEpbrDaJtuyvw86+/26pDVR9yvue+e29DPCXL+HR8+O0KsL8K72NnK+b8iUVhCkV5eXhroVEnc77llJP+gXmz3sS82Qsxb/Z8zJszBwvmzcWMaW+ICvP2W2+yv0+PBSi77OZJVcGFqXIztyO5BpmABzXrNMPGzbkI+gqwfdNq1D4iA2PGjCk1H1a6HNFaUrSw0inLDQkGsXPrJsSnqPSSjtVrtwOBQmRuWYejGtQHJVU6n7+oxMh4D7y93KIdqA+zsrJkwMb6rFOrEbZs3oGiQA42b1mJWrVqWvWpo55d+wrS1vwsKtvgQq0UrYR34smhd1oq3RgsXPyh8DX2XP05wMVklZW1E6nVqklDrJZeBx069kC3rv3QrWsfdOncTVQunTpfie49O6DNxa0lXqzHg2OanYCcwmLrBcyewLL/weXCCy8ERf7Y2FgpK0XKqvw6dOhQ7ogy38tJaT/+c///gXTweJKxI9dWnADeTGxes1zezcYwcvTLMglvg0swH5f882yREusc2RxrNu+ETMaHzCg3K18nt7345fvPUSc1SfJ6bPj/pBLz/GaKn+IzpcXqyaaTXnFtZzi0MWW0ME7K+NDpyvaIiU1GSo0jkVtk5mrMKvJi2ROLq8zjPB5RkXXs1E1G+5ohp4983iK8Nft1pMogIwWvTjHqpfvuukMMPerUbgDO2Tnd5s2bTdshuDz9ogNc2A4DKPTl4O/1K5GeYZhinTq1QLGfu0PUrl0bXCVPuiu4qO98R+nrYrw3azKqeTx44KEhyCsqxuhxE/DIEyNs1SGBhT8x6AoGcOXlBuBiUhvgjw35oAxiBtZs24Iwjg0ogWuv6WDVdRwuOr8tenbti57deqNnt57y69e7D7p27oT27dqiRvUUJFkqIZ7yWr7kYL6myuAivCGEia++hJjEBJGsL7n0GgSKCnHx+Wej87UdhIZ8d/ngbDGZEkSNFlYiQsU3/qAYOIx/ZZwpnycVl7e/VsLatT0fHa+5SuqZFnt8W+Sv4hccmjHYDxLikxAbm4jLLr1cwOWCC1vLfCbZLo1jyq/P8unipLPEdIJLiIPi7RjzzH8tFV08Xnjp5YrAJYB3FpuRF9et9L/OnNJnZ25dhIqN1dL/nn8cGTVjkZIUg4eGDAWNfchWw+a5+x9cnKqSXSG2MjB+erTOryqUv1cux8A+ffD86BeFSvJHa7miHHz67kJjTRebYoOLgIGwqQJc274N4uLTcHSzlhIi9mDWRoiFQV1bVIhff/xSmDxBavhTY8Fa8OrEvTC6EGrXqonYOA/Oa3OJ7PVmwbzdKcOF4xVbTBADenaFJyYJteo1Myo7CweCviJ7Q8YWxzQRptm5a08oTlAlqO6Td2YiWcA1BWMnTpdWQJ3+gH4D8NK4lyUaGTbpyW//8MP3Rd0hkosDXLzefPgDaiIXxIIF0+W96TWqgfMr6enp+OyLrwQAdmblyHcFUdnzTIrx8rOPi5XLRx99hK++/wk9+vRHVp5X8svJyxffCS7Nj2kg74+v3hCb8yFzZqSpsDlREVgMVkC2EPVq15GJ/DpH1Ed+ts9epa+r9VUntfT7bxAf6xG1WNOmTZSMFfpVBRerdPAXZaN7l6sQ64lBnCcBF7VpixbHHWtv5VHhi60WZCskRGI0lKg4bcUxikMF6N29AxI98YiPSUTbS9vh5FNaQs/YUatMJ9PTb6s490MvBtXLXbp0krZJ1fHFF7fFsceeKBaY5muVUrv27ZraprGCi2yy6gcKt2Lm66PNoD0mEYP+7y7hXWwR+ouQXAK48br+MgGYmFod02eblcvO4oWZtR+ntzoByQlGJfb7H3/BF9w1cIlmmaITWc53V/WaYKL56FYeu5JHRaCk6h7mneU15oHcTuTFZ5/FWSc2Q8tmjaQReCxwCRt9cgzsRZ9rr0JcbCqan3A68i0akglTYmBFhRBETs4W/LbsK2HgVD/dcvsDAi58J02YhYbFftTKqC6j4W59+lvQUXK0V/L7Dbjcel0/mVOo3+gEbMkuab3FBYF0jerVFsms/VWdhM0owPAZ5xK+fH8eEggusamY+LrRj9MAQSIbDZIYA1DNyPkFHjFMkCytFmOZiFqkjQFWMh3GjYvx4PY77pA5EbY1ebc05sqDS9/OVyLG48GKFSvQoXNPZOcXioGFdiL6TnCpWyvNGBck1cbf2RC1mHm1EW8CRUaxHSwKykLJjJrVpawdr+pkCqg9zeqtlAg57/Lvh+5DanI8OD82dpwZkOickkkY/b+q4FIU4vwaC+HFts0rUCstCUmxcWJA8ub7H4oqsDLvNeauIaOMEKGNNLcqIXpRKx1qBmhB5O5chzo1jaTK+v7w0y+kLpiRt8hnwVt57bnSrzxoI5IXKb/csmUTqtdIQly8BzGeBLy7+FMxjgnXpyJC1T/Xaq42zSUH6ST88wMFW/Du/MkGXGKTcPk1nSWuNnf6NrgYaSOAs08+GSkyAo2TNQBBmEWTOmLRYi56c4FYJ6UkeNCrRxcJZhtmplIG/ldSLUbLInUqHRDESEQS0/nTeFX1mRd/BJuq/Mjk6ZwSTOS7xdghGEJRXiayfZm4d+iDSE+vjX/16Iu/f1uG3C1/C8OJSaqBp1+YGE5eTMadh97XthfxttnxrWz6qRpJK4tzN2RtF5/RSvJqeuxJNrhYS0ywdu1qo2aJjcHchYtKVbbmpb6pKT/6d+skkktG3aa2JGTUQiEUW2sNjq5fV6Smzt37CNvnR5h6Np/z/WdvidUZJaBXJ80UFZ0/P1vUSzszC3DjoNuQlJKKm265Gd98uwQ0g40OLiwdwYXA4kXAl4mCrE1oWP8IpKUkoEZ6TazbuMmmIctA5qRtxH7guCBY0LHe21/aBtXTUnHDTYOwfvN2W1JhHP6YlxNcqid5UC01UeZcthYaycVu36GgrFVh3pRMnnzsKQHgpEQPXpnwCvzeYGnJBUB25k4pAyUXWsJRWtO2bkpa9n9Z4FLW97MLcj2RuvmzXhe6k/ZXXN1Vgyv0i61aZ7uQn/SjgHWjgaw7Uqe8Hxme/oAiHw0xrNeHCvDGlLGIs+Zw215ytW1cwRjRco12XALjkn+o1FPhxx1EEciHlCexPdPkmHXJX8eO1oCmCt8TjaYapnyC9+Kk2szcL/w7sXDGRBl4xSSm4NquPUS40Kj0S4JLcQBN0jOQ6vGIiMXFZZHgolZj3CGT9vkZNdOwbs1a0ym5jMBqBOGm4Hxd9GvdZVOfsqPQkXhsJNpxNFzjVdUPS11VTWmYV1mpBAgCQcyc8jqS01Nw3GknYe2avxHMLwTydyJ3y1qD8InV8dSo8aoZka1zUJyLnh3aycij6XGnCVsl5Ki6jRVLmpqZlUJ89tZ8ZCQniprtfy8ZdZOO4oc9MlQaWc8+vZHDw6istNpIIn1l4v/q1hExniQouFApRQYrqhwBl2I0qV/bBheWjzVkNzoUg+DCeZmk5Gp4fepMmZBlyWkIkpBYE2e2Ph8rV6+RSVmmzsrNsTpFHEY8+ZwspmR5ufNDsSifClBcTCnQi6mvjUXNtESkJBkTzCuu6SA00TKUBy78DnUcuFBiatasGdZv3CSLv/g82s+AawDpafFmLi3xCGQGgQLL3FK+XjZntVS/QeCBe4eI1M+5t6+++BLevMJS4EIDgPHjxqJGNWOKPXr0KNv8X8tZnl9VcGFe7LMFfs4WBdGl85Vo0pCqvlgZUIx+YUx5r5Nnpt8ZQu5pcJEXBAFfIa1gQujT51rUr5suprQeTxL+94JDzWy1OZbEUa0CzBytk1+Q8XKND3kK7w9FRz6mg/A+ffqIqpjzyDTXfvHFkvSq6PuVlpG+k1fYVFRw8ecBwSy8OX2i9OHUGhmiXo58V0lwQRFqeDyo7olB1269pAKl44oYTM02R0AhLPvpB9l6n2j5yNBHpKa1AFpIU/0aGvlac08iKcPnyE0bCJ86gWR3wOWss86ymJhBd07sV+XXrl07KWxZkku+tZ3IjFenomZSTTQ74WRszNwJn8+aNwjkCriY0UUSHhv5okx8MdOALxfw7Tu8irEAACAASURBVECXKzhpHIOGx7QUcGFKpZxWMrd7EemlqADffvwR6h7VEJ7YeNx8x2BMeO013HHXYLFqGvbYf4WBsx1sy8mR3RJorKw/zY++ARcv9gy4LBZwSUhKwaQ3ZqDYn49ZU18Dd/tt3qIlsnIKZYGi0Z0XgwvkSBOK8yOfHiWjYSmSLbUYSW3Z0s9xZL2aWLrkc9x3z52SJj4xGc++MNoG6fLAxeRp/jmS5ZxN167hEXs0YGGYgsuJTRua9hNTHeuygo4dEQwqyeJIsm2/FwMH/EvMMtOrHYEdW7dB9xjT+Rb6dC1POgFJCfH457lno9BhL1oZZlhVcKExm6+Q5qNePP3UMJza6jRs3LoDJxxvzFm5RokHkGk/NCU0/9LvrIZYDB98RfkCVJSGWFbZPcFGG0t6kZarXCCaLxzKGp4YLyDLHIrAOdxzzmqNTes34dhjj5fNcpNTU7Bh00bqT8xuAmUAjLPceq18Q+8PFV+B5bnnnkPr1q2xYcMGHHvssTKHSbP/suoz2vdHqyGGOfkE78VJ1XFXFgtcpr1i+mNyGgbf+4DGsv1S4JJG87akVNx19/3Skdg4jXbLb40o/bjkkgtl5NP6zHMRLCoWO342YLsQkr0W236XXESCBgNJLK66Hj58OGgGrY2CDV6v1Wd8vaZfkeMZNDRb7d27N3bFFHnIkCHljICKuakGcvMy0bg2mVAsBt/3MHLF5JZlI4P0In/zWotBJZcGl6Jt6Nqe4JIg4EKpwMgcXDVeaFeyDS7BQsx89RV07t4Df677G6++MR0z5s7FgkULkefNFWMKdkTyMa8/AF+IsicXboZQGPTb15HgwnUc5UkuTevVljmVa7v3E3Dk14Xrm5LLYqMW83jw2pSpYq4oqrTYVAwZMlyqyVcUEgaRW5CDnLxcpKTRKjEWTw4fKVvLsD6DwULQYITSSyiYh5YnN8Oo/z0l6bOzM3HiiccjJi5WflSv0ZXXHggUPIKbwMKzKLi9/kMPPWRLhpHgQqBygssVbc4zdedJxnfLNznAxUQ0jJHWOZno0vlqiXt881NkvYuUjdu96Pb7wRBemTBR5o4oufz+y89Sfv2LxuD1mfpVBRf9lm8//xSsj1/++BP5gRCWLVuGGimpYgFIBlWWeknf6y3Mxoq/fjcqLEsNuUfAhfUXAL784iMc06QBVvzxl3A2roviHmoEl3P/eR5y8/NKwRbLpjyA5rnctYE7DmzbZk7GVfWRfsOh4rOd0JT/6KOPxs8/mzb0448/yoCfgwUOqCuqT6Wdcmn6bPt6Xya4kIM4wMVYyHowasxLDn5gKF0KXM5o3kwkl+eeH4081YVKXMOOZs2ZLB3o5JNPMSv3rVJwjyiu/GbhbGfttaUNgOG85gSwAgfDSAgCDM1+O3fuLM+ckgLT6D2vy/vZ794nFwbcVq8xmw/Ge5Jw4213C2NXKQ8565G7aZVhUHHJGPLo06D5MDu9mbTOR8+r2yLek4wmTU+1zflsfLK/g+/y480pk5Hk8eCn335HfqjYHr3b0awLrsB3OppyFvgMbPE6ICoDVp4ft/Tj4sskVE9vKO9nvrLm0lQ5eIpV4zo1RT3Utn1HeadMt3OOjapQXwGWfLAI1eNo/ZQo23ks/+1nJIvuPA633nofsrKLZG2MbnJn5lyMefjwJ54WU2XWK+cfjAoQ6Nj5SnTodBV8gQIEigMygbzk269FFcv5itZn/AM5WZnSXij50kW2DYaR2XCQQHXJHXfcgYcfftgmDcOc8x3O9BRfxo8aiWRZEZ2IxV/9as83SQaBkMyr8LogfzsefWQIkuKr4bSWZ0NOnySw+/2yiSXjrF29Wg4MS69eAx++/75INnZBCNaVUONUBC7sVzqy5YR7UdCL7Tu2ok71ulg06y2pu7wAaQyMeOwJaZdUqTz22GN2UVgO0oT5cEeGxYsX49qO7ZGUHAdd8CqRufmmzY4sthQK4sP338W8ObPEcEGHIFw07HT2fbFf5qAyqtfBaxOnWPmZtvvggw/aWob//Heo1WYhQMMBlDouADWaAY/E58Jdrt0py5HfUEvC75o0aZJcs96jOdKBOydw8Ovcy07jRj53th9e8z2UJFhvZc0BESi4vZFzcBEJDnymYEkzfp4pNHnyZLvN8D0PPPCA0IF9kPWp8Slcan2y3FoO9l263HyzcFiBxemTBQirkpi84qDK7Jf4+IN3yO4KadUz8MVX3zrimXxLgcu9N1wvBaTkwu7K0aZaQy376XvUqJmKk1ueiN9//92oMizJRpiMzLmYw5WEUBa48FVcEc79m1g2NiztAKYYZgKOJ+xRZ8jGrYQm0ZzOiOPhSfnIynTG3VfXmzdvRM3kaoj3JKB+w8b4fdUq2U2X1fL7Nx/g8nP+gZqptIJJxE13GCuv9z/81CxGQgH6dmiLRE8iamQ0FGAic88vUM6uX2HA5ZSjG8k6jZtuvhWzFr2FWQvexLiJL2Pm7FnIzMm25jQUvExakWRCIXnGhWh0BBqxdCraiZt6dUZCTDVk1GpqJBvrlToqRyiApvWOELDo0nOAPNUpYt1sctnn76F2sgcJcXF4ftRorPnrT1nsyZ0H6tRpgvXrzaaENPf96puvccpp/0BcglmTM2TIUJFcvvnmG9N4eQDdmGfRsHEDeAOFInERENU98cjDSK9m1vs8cM+dwsSUOURrD9yTSR0Zyi233CIdgZ1KHbcVmThxYglwYgP/+dsvxLqMdTfsufEa3S4ndz9mm/b78vHe4rfFjLZJo6YygGJ6qsZoSZa1MxMX/PN8pCYlY+7s2eD+YyVOrnTkXN5lReCiaclMjAvhvH+ehX49BhpdhzALY+kV9PtEkiNjpr6etKFz9k0OGslcH3v030hMiMFP1m4KEjEKuAz9z79tRn/WmWcI+JNAXFejTg4ZJMdDAN6CHbjskra4aeAdQkfGCcctllE41dhsK59/Fd4AVNsx+dCll14qe2iRZ7ANcashpom2nY4COE8eJajy2znSp+Tj/G4tKxk5ValJSUk499xzNdj2I59H8ieuzapZs6YMumhKH+kUEFgOPtf5Z/WVD9pAEQrJ9954443SVjU/tnuWn5I58yLAELToCjj3G8URKnTHDn3sBBZelwYXGnEUAKFcDOh6pbyLC6u5qDrSlQKXnz//VEbG6UfUwuqN1HUGUeQvxDtvvwsuhmt32ZXYsGGTjZjsQPwwjjX4M+aJ5kXa4ZUwBCDnbrvSvqwSqVhH/WGkY3oSjn5k5UVjJpHp98X9Jeefb3cqT5xHFpxedM45+EfjOljx/afmWXwy0us2wsXtrsFd9z1k9AHIwuktGiApJhlpNerjk6+WICe8/4Wj6KxmPxpVT0OG7i2UnISENHPQFBsUf/FJiYiNj0O79pfjh2U/ChPVjsjMCDQqwZht33PRtvWpAnwx8bWwYs0mGVSwYanbun6trGpn/ieddra9kJAmrmLMEPJj7qRxYiZdLTUV997/oHzbeWe1RkKcOecnJTUDffoOwHnnX4hGjY/Gu++/Z4NLtbQauOiiNhg2bJi8ctGb85CUGosbb75eVHvcpdls9snHxVi94jfzrTJn48HE8S9pUUuAA9sGmYZ2UN6zDbVv315GlJro77//xqmnnoqVK1eWSM+2HSrIwfnncZ+9VFzb/xZNYrVj6hHCoMetXk48/jgp28TxE2RxKYFn88aNuOqKK1G/Tl18/+13dh57C1wILPxW7i7dq3cXJCTE4KPPvjTSKN8uNgh++Ipy8dzzPEXWI4yWTPnXX3+V8nHkzE+TQWMgCG6DQ1PwEuAiPb4kOzqyfl3Jj3lS9ffosKGyCSoz9es8ZJgCuG5Ab7EC/OKTJYaBkI9YvDBUXICRI58S4GN+terWkTatUgt9blyqjFiz5QaXjP/8889rUCm/Tp069rwxVUlUyYcBORydixUJvAkJCbKVUfiJuYp8HsmPOGBh/gQyzodEusaNGwsQsLz88YwULUekpMS2y/lCxuOefQqUzJPvJR1GjBhh079u3br47Y8/5ZV6JDZvmM45sGJaCbekFGeNlgIXqRw/gpnr0bJJPWt5wGBJH/kXAS5GHJ079Q2kVa+JlPR0dOx8Nc44sxVOb3UWJk+aEZGerZSrpIM2uPD+i08+lM0EWflZO7eKSLgjqxDU1AQD+Vi29Ev8+P1S20KI6jROTnFSKtKR0ERgiqVOgipBIiszMv3evmfn43zT1g3rccY/zCRpTFIcEuJTcPN118siSi6kPLv1mfDEcB+peNzz0FApVo9unXDBGcchLcaDtGSzPiIl/Qhcd/MgfPLpl7B2S7E+wYDL0s8+RrN69aQBxaakID45xW5M2kDVr5mRjh2ZmTLP4aQDwYZ1M2zoEFzdVucUOIqLxcmtzpJNL5f99CeWfv+T7MzconEjs7klO0BidZx+bltcfk1XGa3Mnjsf3bt2RkaKUXHx3dyXrke3Lpgw5kW0aH4S4hNqICm5BlLSaqJTl24CbvleL846l0w7Rjax5KaW7BxD/v0gaqYbSyqC9NWdOoHgQnNrlnnRgjk4rvnRiBeahd958cUXgwOUaO1BOyk7J59zF2XuS0b9PNfd8FQ9joD1ueZB7krz8lcmjocnvhqObH6yRUZ2Ru5ekG8OzFPihoA/f/8Zp592kkhwnTt2AVfk16hWHffedbeAjEblHmS74iojubD8/BZqGAgI3KOteu0MjJvwugBLKN8wk8H33IbkFLN7hY7iOcrmvKfTkRl98O4iWfTJdmG7KJJLrx7dRH2ampwoRgvtLr1EgJhSkjqCzI5tW3BqS9Nf2GZqZ9TBK+MnGR2MsKEg7n/gDilfamqqDJgYr16D+hh06y2y7oX5sWwKLqpKYn0zbjTLKapBSR/uzk3pRtprbCwuu+wyLV4Jf9WqVSAQMR4lnEgX+VzbjvocsHBHCabn3Fak4zQAnxGA6KsBETU2zIOO38edxfl+0oJAV6tWLQFWjcP6phqRQMh89FetRjquv/EmyUfAKOTHti2bseznXznuEYmPO2Jv2ZFlDyqd4OK8ZibmCBEga8NKe46VlpeMpypveZnTFNnUqqXjQrEcnPTi+AmYNnOGdFpVjWlC4zNLtoSQ6KLJ/mZMeV0WQnFPrxWrVqJfnx4iFvYf8H+SZNRzw9H+0nMQHxuLP343O3bywSWXXIJBgwbZI0qCyurVq4UJcMEbGw4nsObPd+xcG2X+pWT59v4dKRB2xXj3g8WYMXc2vvt2qQRzm3y6rVu3Ys68Rfht+Rps3Rle1xNOG/3KrtxQANk5O7Ds+yU475wz5QArTtaTuZvfHMyeOwdvTJ+Olznh382McB594nE7Y06ic65F51zY2ORsEZ7nwsWbXIxZbH46EWzOH6FlVED20ZI4Eea7mg99PufP5Guo8/4Hn2P6zLn4+VcHYwKwfecO2T6co2VKpuwoPPmR5sgB0JjBL61L1k/J/LkZzBiJyxy2JdeW9Kwd2umzTM4fpRj+uH3MO++8Y6sOSCRKOSVdCDxcjMcYND/2OFl4aFR3JpY3P9da52KYgPRW5rNzBz7/5HNMenUyPv7wI1vdk59jdopWmoof0YZLvr/0XUXgot/OlLxmxXLwR2DmQEi4AMkoYaUNZjS9+LQKs4rw5oJZSI6PwQ8/O+qQ4MKGE/GbP3cO1qz6Cw/cd68MMqjmcmoshCCaxi6Q4LWtupM87beXpkNZIazrpUuXCkMn/4h02s4YvmjRIpHUOB/H/eqiOZ0z4eBWJQpnvMjnJehnqapYDtZbpIqf+TCMxwmwD3AukGAj9WY9c74r2rXGVT9anHBYMW67rpcMZvv9awAee/JpqR9uhNnk5NbYmGMOIAzHt5tLuCZYb5yve/wRAbDrrrvOfkbaO50tuZhAZWWOTB3zH86E4fhG2qEOnq9dv2YlaiTHieTy2BNPSjSeuTxg4F0Y//I0fPPl+/jmi8VSsHcXfyy6aSJzcrV02XHX7y0AGTKR9dTTzsT27Ttt8a958+ZSEVoOVkxkZeqz/emzIwuhLZ6jZWHn1m2pNUx9UT/Yayg0lJv1BWSURqb718o/ULtOOr77bokwC8ai1Gd+QQENhmkV33LbrbJoMZwbGT8BIPzTPq6gwPLxWsOVEeq9+ho/0tf0znfqNb9Ry6bldHYKnvpIazEdsDA24wttZIsXwyhtcNHCVAFcFGgUZLTD672W1fimP+TnZuKrr76QkS63OJeyB4pk7tDuKazriPpmPJnYN5lhX4KL9gtz8mVpIxgBG8e2ORq/hG8tKmXx355vwGXpT7/bdcgDz+yGonXB+rKklGs7XC2br9oDmEBEfOakdCvLt2hXWY/gQSbNuYzKOLYHMvTx48fbfKYy6cqKU4J+ZRgJRKZV0CLAsRxsi3vHBYHsjTiuQTqaHtMcazdsFq793vuL4Umri6lvf1bSYCU8FpE6d/ZdrhejUcGGTcwjuosAl+iRooeajqfsguTgb8yo53Bs08Z4/nmzk+nmjesESB59fDTe/5ATtkE8/ODtOOrIRmLWSEujt99ciPiMI5FNyZn7ShXuRIOjGmHipGnIKzAKWE5g0ZpMnVbIrlSm5rHH/RBNk0tzGIqs3L6CIEBmTGapjuVnA1eGL8CkDzl68ReJGongQjVH8+ZNRZfOeHkF5atWKL28OLak1Yy+R33lCZEgoeHKjO17a6AaGV/vFVzYQfjdAo4+v4jMzsapn8j8yeA5r2faUiSXCVkDCAMsHHGX/JVmnM42YZc/QoLRcJaDgxtNo+UyvpY4KBLVnXfeKeoLmvGGT8t0MEhnYv0Mhln1LVaS3PGBhi7WT9+rvjOLaNeVlVw0v93yHW21suBCKYXgQuOGM08/TSzB+B004pGJejYkm1U5aKf0ivSjEaGcMBpmqIqL9VqRe//992VhrapOo8WviNlX9Jz9oCJHVe2JJ55YJamlojz1ubZiw6G9OPekprhuwPWibkbIh/zcbHiSa2HE+Dcc4GJS8d/5Y3uidR7Vb7RWIx9Rx2fO0UK54MIOSMKURzyToTXaBWQXUy4S46Q/n7368kug6eVrk81+Uzzj5KLzTkOvnn1MmUI+3HTDQJx3VQ/TB4N5ePW5R+Uwp4078/DapCm49dZbQb0gHctEYNFy8R3On37o/vZZRpaLIymnU0lDmZv6yuwjwUXTTp/+BlLTkpFxRE0sX/6HPY/CunH+mB8drceOad5M1pNoHnyi71FfQUPBQX0N1/LZ95UEF+bPtPxedbQU04aqYeobcNE7MiCmM7FLgsmeBReWUesoOjMKl591euWVV4pFjg0uYqRiaK6lZ9FpJca94ejMDtPmkygJKrDQd7ZdXlfkFFzY/ln2yPR7+p7tgY7gkhTngVNy4Xk0kZIL56EILBf88zysXrnC/hxKL2IlZrcAqyXwk8v72TlU7oJzaaoOI30iHetaw6kWu+iii8SqrCwAKK0qLZljRc+pfq3Iffjhh2IBRus29mW2Q5aH80N71gWBwh04o0Uj3HCDmYdh/jnZO+DxpGH42CkCLqYdhtuiVVNSc6QtrXqfeOIJKZpuKBouZ7gyIw4LC0fRK2dj1TD19RnvVa9aq049DL77HgMAPi/69eqJI2qmY+MWQ+QNa1ehdo0UObLT5BNAvTq17A9DIBc397wKx51wEqbMXiiSCxsDf8pEOdLVMPWdZdHy7W/fVFL0Umh5Kyq/NjAaM9AckhOvnGDk5B11tXSki3YOWsoMGDAATZs2xWeffVbi5Xynvs/2S6vMI/lFufcKRhX5otqy1GKlu7yzmGyc4eZcPrAQaEoz6N0Jc5Yk2jVpTdUYmdKWLVvkDBcFCwGOaImcYfJ5YcnF+agy15wn4gQx608Bxq7LvQA2Ci7vLporpui//mmOQeY7pWE46or1dvutN4sqLGwZFq7LaPHLBZYwnyobgCyisV7uu+8+WVPCIClfFIIynHG53omWWZFtJUqS3QqqKH+e48Ny6ABnt15WYWIDLqc3Pwo3D7rVih3Aho1r4YmviRcmz0dWgZqwW3N2GisEUYG1atVKgIV8SVXKJV8brrQqgQsJpU6bjBmYFqPYl4clX36GuKRUfPr19yZaKIhjGjXEfffcIyalDFwwexbq1KghZ3Pw/q/flolVybe/r0WWqNu9aH1iE5zyj1ZmnY1jMSBXo7JDsXFoWSqqPC3vgepXpvw6oqY+Vk92VGsQWveo1YuGUR9KIwin43ucTMi+3sfgQsmMv7IdR+OR0kl59/sWXLRDvf7662L9s3KFYba2dFL2h4WfONRi4cDKXXFAQYsh1l95g6zIdrWr9yp5vrNgNpJiPFi+aq1sUBj+XuUE6ps1LVGllAggkkFEmBeVDSDlxbEmvjnPQnUlHXkEpUyuMSnLkX7RaFJW/F0Nj3xHtHwYh07jRouzR8K4i3XeVpxw1BEYPPhucO9IBLgPWz48MdVELWa/x9FFuUbxw48/Rbv2V4gRjMbRvqD3xg9X1i6DCzNic6ITS5CiHPzn/rtwwqmni4UPw5d+8zWqJyfh159/ATeHobKjf68+aNfmMrESogXV/557Bo0bHYU16zfh2++XobjIhyH334OaGUdgzNgJsgCIjHLo0KFiiuwEFnl3xMhVCnQQ/WmDUj+y6Pxep6NOmVILzWcJJmrCyMm1bt26gTpkdSrNaN70bVDROQgXXOxOTfpUxmmdcAHdjGnTzYLJyiU12Yf7X2VeVyIOjyDXBXSsX2fd7o1rSi5sM/NnTENijAdLf/hZwIXzR+aENwUV43NuxZZaIudX9hK4cC7s5ptvFkmeakMOwrj+hYsrnY70IUMk3XQn9kiaOePvievy8mc7UvU5/b3uCC7FeTilSb0SajHu4EC12BNjJiPXPs6eDN40aqqzX5rwsswXaxnZJrQfaJjxw417t8BFM5WXBL247KLzcOd9D9mg8+8H7sdJxx4vuuecwlxZkNn2gjZo1fI02ROHevnBg+9A/QZ18csvv9iFpR6zV69eNvOk6KgTbqwspyuv8pzxDtTrypSf9GWniPx2hlVGnHa+wwWX8iWd8toJ6UjGVKpTUcslzLa81I5n4f7nCKzcJd+tjJEpnHW7N66JD1OnTkXPTh0FXHr27o8vvvnObF0TCR7OiTlKp3ofDVQ0zEmLXbjmEeYqsXOgpYMthg0eXHJxH+lDp/UXjV6Vq4XKx4p8R7SUzvJEe77nwooxZdz/cEQyd70/HgsWvo11a1aLWs7jicNFV3XFZ18tsXmKrhui9KrbSSkf1jKXLlu4EisEl9KJS4eYSjMjFx3HmFiWNYhlScZn2qYiLktn6oZUigLaeMuLrHGi+ToXsq98bR/ql1fuA+2ZaecRpQr3pehqHWf0iuLuynOnio3Xu5JHOWm4aa3Jk33ZPmNWpJkK1Vp7oTx74vtkbqycb94T79jlPPY0zUq1P25XJJzYCAEWHRiidnzOJBVel0PH3QaXspmE9YQvdxac9+bbbJyxbiO+o+ycIyIe1rcKGBURQeNF+vsKVPQ9WqvqV1TuA/55OZ1LGIzzAyqKuyvP9xO4mM+qwJR4TzPKXaFPtDQHarmilXV3w5ztj9ean4ZH3mt4ZX1NH8XfbXCpsAx8qVNg4b0DTQ4ZJlMhIfZOBAWLXc1dmf6+8rW+1d/Vch8w6aJ0KrsDHwrPSGj5jrAWwu6+DNch4sH0rS64hLuP1ls4pGpXmj6Kv3/AhQWx3CHDZPSD9rHvgss+Jnjk66J0qkMdXIQE+t0HI7ho2Q8Hv6z2quFKA72vqq/po/h7H1yswtogooWo6ke48StFAVqdqJUY9yui9Qw3zytrAq6ietGFj7Qa2rJtBxa++ZbsZfbjTyUPutLCqQQkB8xZK7w1jL6+T31Nd9D62p4PeT8suUhdHfLfqxLbIeprh9N61Puq+po+ir9PwcUuNwviur1CAVqDbd++XU7epPn22LFj5cx454aLUV+sjSPKw5Wr16B7z964qE1bTJ76BqbPnI0Hh/wbLU89TSyJNAkBQ4HEBZdDjSk55ldY4dpeXP/gpIV2Wq0/va+qr+mj+PsMXKpaZjd+5ShAhi7OqlxKF81aHAseE2tWjIdw9+A7SuzLpklK+No4SgQCS75biiMbHo1HHntCdkvYmZUjMXh08O9/Lpcdr3mGhDobXKz1R3qvvkos6mu6g9ZXurn+wclkD/d6292OVw79XHDZXeLu5/RhcDHs+ozWZ8tW2s5iPfnYMNky3hlmX2vjYHJe287k16RZU5x1znlykigf6XYgvKaU9OzIp2WdweIPPpYFWAoiOhek9+qbXMPqMft1B+uF0s/1XXA5GNvA7va7cr7ZBZfdJe4BkF63YXhmxDDUbtAA67fuMPMu/kIE8nZgYP/eaHJiK3AbPB68pYujjL07W0dJCz5j8R7Ac6MeFeAYM2Zcqa8kWNDxvBPuedb8lNbYWaSnkYYXKiqoqO+Ci6tSclVqB1AbKNWzqxjggksVCXaQRCejVrdtwypk1EjEjbfcjkLng6IcNGt8FFq3vQpZ1mFgsvW5tT3P1Ze3Q2pCEuI88XL+e6wnFilJMcgrXIdzzj8OqWmJWLbsZ1AdtvRHs3cTVWJ03CacrlmzZvCk1Mafm/IQ4Do+x5Y8Cirqu+ByADGWchiDCwCHST1JD96Nv3LakCu57AZd92dSZdK6CeTwYQ8jzuPBv4c+jsnT5mDmzOmYP/sNTBj9tBxHeu/Q4Y6zGoKYPXM6/nFKSyxetBDB/EIjrDi2Nyr0b0SNDHNc6orlK7Fm3Xpc2q49Zs6egwWL3pQJfdl2O1Ao29B7EtIx5/1vHOBiNhdVUFFfy63+/qThHnl3OZ3LZdCHCYM+mNvA7naCcr7dBZfdJe5+Tc+jCIpQDD9aNG2BFsecgGnTF2DuvLcxZeokLFo4Ax2uaIO0lCT8+Mcq2VCUG4MGvTk455xzsHKldQwsd0elpZcl8vi9OSjGph88vQAABEFJREFUdqTWMOCybdsO5OYXIDY+UdRk8Yk87zsGw4cPp15Mjqj2xFbHtLc+c8GlnM7mgo0LNgdcG9hd/lVOe3fBZXeJu1/TBxBCHpav+AUeTxLuvvtR8OTZwnxz8l2BdweOOrIu2rRp49gUwY+/flkqRxrMmr0Qi+bOx/wZs/DmvLcw+405mDN9NmZMfRVALpo1TxcwWbvmb/D3+GPD5WuDgWL89tsfmDh+As+0xemnny67qn7z23obXPQgLJVY1FeJRf39Sr498fJyOtcBx0jcsrpGB5FtYHf7QGR+jnsXXHaXuPsrPStRZJEczJw7GbFJdTBl6gcIWofXFcOHVyaNNZZc75lt+GXnXvix4sev0az58ejScwB6duuJ7h07o0+3vuhyTRcM7DsA1/XrASALN97USdLPnj0XWZk5yMsrQKHX6M4IMJk7dgi48HyRtAbNxWBA51zsA7QiFlIqqKi/v8i3x97r6EwumLiSyUHXBna3I5TT/l1w2V3i7tf0ZPSZGDNuJDzx9fDTr5lmZOYrRlb2Vpxyxkm46toOsrAxr8A6bjl/G7LWL8cJLf8BrwBUyQ8oyM6XgGBoC37+5SMkJcehX79/oagoIOEEGHUEq4Vz5oiKbMTYSQJ1Lri4DPagY7DlMMhD/lu0M++qXw7tXHDZVaIeEOnI8LMxddrL8HiSsWa9D/CZgo164WlccMl52LJzu0MlRmEnl2f3of/AG9G97/VijRwsDMjCE3++AZCgT4yWebo2Rjz1OJKSUrBkyXfw+XiWSRiR/IU+nHLiCXIoE6HLaYqsajGu1FeVGH2VWNQ/IMi4O4Uop3Md8ozJ/faDX822O22factpAy647C5x92v6MItudHRTjB33OnwFATz5+BNo0/YCbNu52WbmpphW/FAQWXn5uH7QbUhMSEbnjl3Qr0d/dO3QDd07dUPfHj2Qn0spyMzdvPjCaDmE6dlnn7XPzf70009xzllnY2C/vuGTByOXy+xX2uyjl5fTucrreO6z8hmTS5+Dnz4uuOwjHrS3X8Pjj3l6Z+dOXa1zrsn1wpKCvl83sOTJcjxhjidZ8qjeuTPmyG/B7Dl4Z+Ei5OfkmmNOrVMW161bh9GjR+Oaa65B9+7dMWTIECxZssTRA+wziPRVh4fvgku5o1cXJBxd5DBrKy64HCIsUM/i5ucQQKKdcc3FjRrOVf3Oc7uLfUFQPVZc5Af8Qfv8bDKHoN9IMMxXwSmcNoSg3yfhfn9QTrY9REhauc84zBiGCxaHL1hUte5dcKkcCzlgYxEs6HQLGC2ohut9pK/xfd5COQ/dX+BYQUlwUWcEILkjOBFUKO04XcDnSOt8cDhcu+DiSi5uG4jaBlxwORwYYHnfqB1Dp2/0Xv3ItBqufuTzw+1e6eD6URlMVUe7bvxDRzJyweVwY4aR36tM0QWXSMpU7l7p5/ouuLhtoEQb+H/EkFLa6JDvQAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里讨论的是2次采样的情况，当然也可以拓展到多次采样的情况：\n",
    "![image.png](attachment:image.png)\n",
    "最大似然估计的公式（n次采样）"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们定义M为模型（也就是之前公式中的f），表示抽到白球的概率为theta，而抽到红球的概率为(1-theta)，因此10次抽取抽到白球7次的概率可以表示为：\n",
    "![image.png](attachment:image.png)\n",
    "10次抽取抽到白球7次的概率"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将其描述为平均似然可得：\n",
    "![image.png](attachment:image.png)10次抽取抽到白球7次的平均对数似然，抽球的情况比较简单，可以直接用平均似然来求解"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "那么最大似然就是找到一个合适的theta，获得最大的平均似然。因此我们可以对平均似然的公式对theta求导，并另导数为0。\n",
    "![image.png](attachment:image.png)\n",
    "求导过程\n",
    "由此可得，当抽取白球的概率为0.7时，最可能产生10次抽取抽到白球7次的事件。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上就用到了最大似然估计的思想\n",
    "\n",
    "令Dc表示训练集D中第c类样本组成的集合，假设这些集合是独立同分布的，则对参数θcθc对于数据集Dc的似然是:\n",
    "\n",
    "$$P(D_c|\\theta_c) = \\prod P(\\mathbf{x}|\\theta_c)$$\n",
    "对$θ_c$进行激发似然估计买就是去寻找能最大化似然函数的参数值$θ_c$.直观上，极大似然估计是在试图在$θ_c$的所有可能的去职中，找到一个能使数据出现最大“可能性”的最大值。\n",
    "\n",
    "上面的式子中的连乘操作容易造成下溢，通常使用对数似然：\n",
    "$$L(\\theta_c) = \\log P(D_c| \\theta_c) = \\sum_{x\\in D_c} \\log P(x|\\theta_c)$$\n",
    "此时，参数$θ_c$的极大似然估计$\\hat{\\theta_c}$为\n",
    "$\\hat{\\theta_c} = argmax_{\\theta_c} LL(\\theta_c)$\n",
    "例如，在连续属性的情形下，假设概率密度函数$p(x|c) \\sim \\mathcal{N}(\\mu_c , \\sigma^2)$,则参数$μ_c$和$σ_2$的极大似然估计为：\n",
    "$\\hat{\\mu_c} = \\frac{1}{|D_c|} \\sum_{x\\in D_c} x$\n",
    "$\\hat{\\sigma_c}^2 = \\frac{1}{|D_c|} \\sum_{x\\in D_c} (x-\\hat{\\mu_c} )(x-\\hat{\\mu_c} ^T)$\n",
    "也就是说通过极大似然发得到的额正态分布均值就是样本均值，方差就是$(x-\\hat{\\mu_c} )(x-\\hat{\\mu_c} ^T)$的均值。这显然是一个符合只觉得结果，在离散属性情形下，也可以通过类似的方法来估计类条件概率。\n",
    "\n",
    "需要注意的是这种方法虽然能够使类条件概率估计变得简单，但是估计结果准确性严重依赖于所假设的概率分布形式是否符合潜在的真实数据分布。在显示生活中往往需要应用任务本身的经验知识，“猜测”则会导致误导性的结果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "贝叶斯分类器的训练过程就是参数估计。总结最大似然法估计参数的过程，一般分为以下四个步骤：\n",
    "```\n",
    "1.写出似然函数；\n",
    "2.对似然函数取对数，并整理；\n",
    "3.求导数，令偏导数为0，得到似然方程组；\n",
    "4.解似然方程组，得到所有参数即为所求。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 朴素贝叶斯分类器\n",
    "基于贝叶斯公式来估计后验概率P(c|x)主要困难在于类条件概率P(x|c)是所有属性上的联合概率，难以从有限的训练样本直接估计而得。\n",
    "基于有限训练样本直接计算联合概率，在计算上将会遭遇组合爆炸问题；在数据上将会遭遇样本稀疏问题；属性越多，问题越严重。\n",
    "\n",
    "为了避开这个障碍，朴素贝叶斯分类器采用了$“属性条件独立性假设”$:对已知类别，假设所有属性相互独立。换言之，假设每个属性独立的对分类结果发生影响相互独立。\n",
    "\n",
    "回答西瓜的例子就可以认为｛色泽\t根蒂\t敲声\t纹理\t脐部\t触感｝这些属性对西瓜是好还是坏的结果所产生的影响相互独立。\n",
    "\n",
    "基于条件独立性假设，对于多个属性的后验概率可以写成：\n",
    "$$P(c|\\mathbf{x}) = \\frac{P(C)P(\\mathbf{x}|c)}{P(\\mathbf{x})} = \\frac{P(c)}{P(\\mathbf{x})}\\prod_{i=1}^d P(x_i|c)$$\n",
    "\n",
    "d为属性数目，$x_i$是x在第i个属性上取值。\n",
    "对于所有的类别来说P(x)相同，基于极大似然的贝叶斯判定准则有朴素贝叶斯的表达式：\n",
    "$$h_{nb}(\\mathbf{x}) = \\arg max_{c\\in \\mathcal{Y}}P(c)\\prod_{i=1}^d P(x_i|c) \\quad (1)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. 极值问题情况下的每个类的分类概率\n",
    "极值问题\n",
    "\n",
    "很多时候遇到求出各种目标函数（object function）的最值问题（最大值或者最小值）。关于函数最值问题，其实在高中的时候我们就已经了解不少，最经典的方法就是：直接求出极值点。这些极值点的梯度为0。若极值点唯一，则这个点就是代入函数得出的就是最值；若极值点不唯一，那么这些点中，必定存在最小值或者最大值（去除函数的左右的最端点），所以把极值代入函数，经对比后可得到结果。\n",
    "\n",
    "请注意：并不一定所有函数的极值都可以通过设置导数为0的方式求 出。也就是说，有些问题中当我们设定导数为0时，未必能直接计算出满足导数为0的点（比如逻辑回归模型），这时候就需要利用数值计算相关的技术（最典型为梯度下降法，牛顿法……）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. 下溢问题如何解决\n",
    "数值下溢问题：是指计算机浮点数计算的结果小于可以表示的最小数，因为计算机的能力有限，当数值小于一定数时，其无法精确保存，会造成数值的精度丢失，由上述公式可以看到，求概率时多个概率值相乘，得到的结果往往非常小；因此通常采用取对数的方式，将连乘转化为连加，以避免数值下溢。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7. 零概率问题如何解决？\n",
    "零概率问题，就是在计算实例的概率时，如果某个量x，在观察样本库（训练集）中没有出现过，会导致整个实例的概率结果是0.\n",
    "\n",
    "在实际的模型训练过程中，可能会出现零概率问题（因为先验概率和反条件概率是根据训练样本算的，但训练样本数量不是无限的，所以可能出现有的情况在实际中存在，但在训练样本中没有，导致为0的概率值，影响后面后验概率的计算），即便可以继续增加训练数据量，但对于有些问题来说，数据怎么增多也是不够的。这时我们说模型是不平滑的，我们要使之平滑，一种方法就是将训练（学习）的方法换成贝叶斯估计。\n",
    "\n",
    "现在看一个示例，及$P(敲声=清脆|好瓜=是)=\\frac{8}{0}=0$\n",
    "不论样本的其他属性如何，分类结果都会为“好瓜=否”，这样显然不太合理。\n",
    "\n",
    "朴素贝叶斯算法的先天缺陷：其他属性携带的信息被训练集中某个分类下未出现的属性值“抹去”，造成预测出来的概率绝对为0。为了拟补这一缺陷，前辈们引入了拉普拉斯平滑的方法：对先验概率的分子(划分的计数)加1，分母加上类别数；对条件概率分子加1，分母加上对应特征的可能取值数量。这样在解决零概率问题的同时，也保证了概率和依然为1：\n",
    "$$P(c) = \\frac{{|{D_c}|}}{{|D|}} \\to P(c) = \\frac{{|{D_c}| + 1}}{{|D| + N}}$$\n",
    "$$P({x_i}|c) = \\frac{{|{D_{{x_i}|c}}|}}{{|{D_c}|}} \\to P({x_i}|c) = \\frac{{|{D_{{x_i}|c}}| + 1}}{{|{D_c}| + {N_i}}}$$\n",
    "\n",
    "其中，N表示数据集中分类标签，$N_i$表示第$i$个属性的取值类别数，|D|样本容量，$|D_c|$表示类别c的记录数量，${|{D_{{x_i}|c}}|}$表示类别c中第i个属性取值为$x_i$的记录数量。\n",
    "\n",
    "将这两个式子应用到上面的计算过程中，就可以弥补朴素贝叶斯算法的这一缺陷问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "用西瓜的数据来看，当我们计算\n",
    "\n",
    "P(好瓜=是)时，样本有17个，所以|D| = 17，N，好瓜标签可以分为｛是，否｝两类，所以N=2，（好瓜=是）的样本个数有8个，所以这里$|D_c|$=8。\n",
    "\n",
    "综上，根据拉普拉斯平滑后有 $$P(好瓜=是) = \\frac{{|{D_c}| + 1}}{{|D| + N}} = \\frac{{|{8}| + 1}}{{|17| + 2}}$$\n",
    "P（色泽=青绿|好瓜=是）时，色泽青绿的样本有8个，所以|D_c| = 8，N，色泽标签可以分为｛青绿，浅白，乌黑｝三类，所以N=3，（好瓜=是）的样本个数有3个，所以这里$|D_{c,x_i}|$=3。\n",
    "综上，根据拉普拉斯平滑后有$$P（色泽=青绿|好瓜=是）= \\frac{{|{D_{{x_i}|c}}| + 1}}{{|{D_c}| + {N_i}}}=\\frac{{|{3}}| + 1}{{|{8}| + {3}}}$$\n",
    "同理，分析可知，之前不合理的$P(敲声=清脆|好瓜=是)=\\frac{8}{0}=0$在进行拉普拉斯平滑后为$$ P(敲声=清脆|好瓜=是)= \\frac{{|{D_{{x_i}|c}}| + 1}}{{|{D_c}| + {N_i}}}=\\frac{{|{0}}| + 1}{{|{8}| + {3}}}$$显然结果不是0，使结果变得合理。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8. sklearn参数详解\n",
    "1. 高斯朴素贝叶斯算法是假设特征的可能性(即概率)为高斯分布。\n",
    "```\n",
    "class sklearn.naive_bayes.GaussianNB(priors=None)\n",
    "参数：\n",
    "priors:先验概率大小，如果没有给定，模型则根据样本数据自己计算（利用极大似然法）。\n",
    "var_smoothing：可选参数，所有特征的最大方差\n",
    "属性：\n",
    "class_prior_:每个样本的概率\n",
    "class_count:每个类别的样本数量\n",
    "classes_:分类器已知的标签类型\n",
    "theta_:每个类别中每个特征的均值\n",
    "sigma_:每个类别中每个特征的方差\n",
    "epsilon_:方差的绝对加值方法\n",
    "# 贝叶斯的方法和其他模型的方法一致。\n",
    "fit(X,Y):在数据集(X,Y)上拟合模型。\n",
    "get_params():获取模型参数。\n",
    "predict(X):对数据集X进行预测。\n",
    "predict_log_proba(X):对数据集X预测，得到每个类别的概率对数值。predict_proba(X):对数据集X预测，得到每个类别的概率。\n",
    "score(X,Y):得到模型在数据集(X,Y)的得分情况。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据李航老师的代码构建自己的朴素贝叶斯模型\n",
    "\n",
    "这里采用GaussianNB 高斯朴素贝叶斯,概率密度函数为\n",
    "$$P(x_{i}|y_{k}) = \\frac{1}{\\sqrt{2\\pi\\sigma_{y_{k}}^{2}}}exp( -\\frac{(x_{i}-\\mu_{y_{k}})^2}  {2\\sigma_{y_{k}}^{2}}   )$$\n",
    "数学期望：$\\mu$\n",
    "方差：$\\sigma ^2=\\frac{1}{n}\\sum_i^n(x_i-\\overline x)^2$\n",
    "\n",
    "https://github.com/fengdu78/lihang-code/blob/master/%E7%AC%AC04%E7%AB%A0%20%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF/4.NaiveBayes.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "class NaiveBayes:\n",
    "    def __init__(self):\n",
    "        self.model = None\n",
    "\n",
    "    # 数学期望\n",
    "    @staticmethod\n",
    "    def mean(X):\n",
    "        \"\"\"计算均值\n",
    "        Param: X : list or np.ndarray\n",
    "        \n",
    "        Return:\n",
    "            avg : float\n",
    "        \n",
    "        \"\"\"\n",
    "        avg = 0.0\n",
    "        # ========= show me your code ==================\n",
    "        avg = sum(X) / float(len(X))\n",
    "        # ========= show me your code ==================\n",
    "        return avg\n",
    "\n",
    "    # 标准差（方差）\n",
    "    def stdev(self, X):\n",
    "        \"\"\"计算标准差\n",
    "        Param: X : list or np.ndarray\n",
    "        \n",
    "        Return:\n",
    "            res : float\n",
    "        \n",
    "        \"\"\"\n",
    "        res = 0.0\n",
    "        # ========= show me your code ==================\n",
    "        avg = self.mean(X)\n",
    "        res = math.sqrt(sum([pow(x - avg, 2) for x in X]) / float(len(X)))\n",
    "        # ========= show me your code ==================\n",
    "        return res\n",
    "        \n",
    "    # 概率密度函数\n",
    "    def gaussian_probability(self, x, mean, stdev):\n",
    "        \"\"\"根据均值和标注差计算x符号该高斯分布的概率\n",
    "        Parameters:\n",
    "        ----------\n",
    "        x : 输入\n",
    "        mean : 均值\n",
    "        stdev : 标准差\n",
    "        \n",
    "        Return:\n",
    "        \n",
    "        res : float， x符合的概率值\n",
    "            \n",
    "        \"\"\"\n",
    "        res = 0.0\n",
    "        # ========= show me your code ==================\n",
    "        exponent = math.exp(-(math.pow(x - mean, 2) /\n",
    "                              (2 * math.pow(stdev, 2))))\n",
    "        res = (1 / (math.sqrt(2 * math.pi) * stdev)) * exponent\n",
    "        # ========= show me your code ==================\n",
    "        \n",
    "        return res\n",
    "        \n",
    "    # 处理X_train\n",
    "    def summarize(self, train_data):\n",
    "        \"\"\"计算每个类目下对应数据的均值和标准差\n",
    "        Param: train_data : list\n",
    "        \n",
    "        Return : [mean, stdev]\n",
    "        \"\"\"\n",
    "        summaries = [0.0, 0.0]\n",
    "        # ========= show me your code ==================\n",
    "        summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]\n",
    "        \n",
    "        # ========= show me your code ==================\n",
    "        return summaries\n",
    "\n",
    "    # 分类别求出数学期望和标准差\n",
    "    def fit(self, X, y):\n",
    "        labels = list(set(y))\n",
    "        data = {label: [] for label in labels}\n",
    "        for f, label in zip(X, y):\n",
    "            data[label].append(f)\n",
    "        self.model = {\n",
    "            label: self.summarize(value) for label, value in data.items()\n",
    "        }\n",
    "        return 'gaussianNB train done!'\n",
    "\n",
    "    # 计算概率\n",
    "    def calculate_probabilities(self, input_data):\n",
    "        \"\"\"计算数据在各个高斯分布下的概率\n",
    "        Paramter:\n",
    "        input_data : 输入数据\n",
    "        \n",
    "        Return:\n",
    "        probabilities : {label : p}\n",
    "        \"\"\"\n",
    "        # summaries:{0.0: [(5.0, 0.37),(3.42, 0.40)], 1.0: [(5.8, 0.449),(2.7, 0.27)]}\n",
    "        # input_data:[1.1, 2.2]\n",
    "        probabilities = {}\n",
    "        # ========= show me your code ==================\n",
    "        for label, value in self.model.items():\n",
    "            probabilities[label] = 1\n",
    "            for i in range(len(value)):\n",
    "                mean, stdev = value[i]\n",
    "                probabilities[label] *= self.gaussian_probability(\n",
    "                    input_data[i], mean, stdev)\n",
    "        # ========= show me your code ==================\n",
    "        return probabilities\n",
    "\n",
    "    # 类别\n",
    "    def predict(self, X_test):\n",
    "        # {0.0: 2.9680340789325763e-27, 1.0: 3.5749783019849535e-26}\n",
    "        label = sorted(self.calculate_probabilities(X_test).items(), key=lambda x: x[-1])[-1][0]\n",
    "        return label\n",
    "    # 计算得分\n",
    "    def score(self, X_test, y_test):\n",
    "        right = 0\n",
    "        for X, y in zip(X_test, y_test):\n",
    "            label = self.predict(X)\n",
    "            if label == y:\n",
    "                right += 1\n",
    "\n",
    "        return right / float(len(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = NaiveBayes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([4.7, 3.2, 1.6, 0.2]),)\n",
      "(array([4.3, 3. , 1.1, 0.1]),)\n",
      "(array([5.1, 3.8, 1.6, 0.2]),)\n",
      "(array([4.8, 3. , 1.4, 0.3]),)\n",
      "(array([5.1, 3.7, 1.5, 0.4]),)\n",
      "(array([4.7, 3.2, 1.3, 0.2]),)\n",
      "(array([4.4, 2.9, 1.4, 0.2]),)\n",
      "(array([5.2, 3.4, 1.4, 0.2]),)\n",
      "(array([5.1, 3.4, 1.5, 0.2]),)\n",
      "(array([4.6, 3.4, 1.4, 0.3]),)\n",
      "(array([4.6, 3.6, 1. , 0.2]),)\n",
      "(array([5. , 3.5, 1.6, 0.6]),)\n",
      "(array([4.9, 3.1, 1.5, 0.1]),)\n",
      "(array([5.7, 3.8, 1.7, 0.3]),)\n",
      "(array([4.6, 3.1, 1.5, 0.2]),)\n",
      "(array([4.9, 3.6, 1.4, 0.1]),)\n",
      "(array([4.8, 3.4, 1.9, 0.2]),)\n",
      "(array([5.1, 3.5, 1.4, 0.3]),)\n",
      "(array([5.1, 3.8, 1.5, 0.3]),)\n",
      "(array([5.3, 3.7, 1.5, 0.2]),)\n",
      "(array([5.4, 3.9, 1.7, 0.4]),)\n",
      "(array([5. , 3.4, 1.6, 0.4]),)\n",
      "(array([5.4, 3.7, 1.5, 0.2]),)\n",
      "(array([5.1, 3.5, 1.4, 0.2]),)\n",
      "(array([4.9, 3. , 1.4, 0.2]),)\n",
      "(array([5.7, 4.4, 1.5, 0.4]),)\n",
      "(array([4.8, 3.4, 1.6, 0.2]),)\n",
      "(array([4.4, 3.2, 1.3, 0.2]),)\n",
      "(array([5. , 3.3, 1.4, 0.2]),)\n",
      "(array([4.6, 3.2, 1.4, 0.2]),)\n",
      "(array([5.4, 3.4, 1.5, 0.4]),)\n",
      "(array([5.1, 3.8, 1.9, 0.4]),)\n",
      "(array([4.5, 2.3, 1.3, 0.3]),)\n",
      "(array([5. , 3.5, 1.3, 0.3]),)\n",
      "(array([4.4, 3. , 1.3, 0.2]),)\n",
      "(array([5.2, 3.5, 1.5, 0.2]),)\n",
      "(array([6. , 2.7, 5.1, 1.6]),)\n",
      "(array([6.1, 2.8, 4.7, 1.2]),)\n",
      "(array([6.6, 2.9, 4.6, 1.3]),)\n",
      "(array([6.4, 2.9, 4.3, 1.3]),)\n",
      "(array([5.8, 2.6, 4. , 1.2]),)\n",
      "(array([5.5, 2.5, 4. , 1.3]),)\n",
      "(array([5.5, 2.4, 3.8, 1.1]),)\n",
      "(array([5.6, 2.5, 3.9, 1.1]),)\n",
      "(array([5.4, 3. , 4.5, 1.5]),)\n",
      "(array([6.4, 3.2, 4.5, 1.5]),)\n",
      "(array([5.7, 2.8, 4.1, 1.3]),)\n",
      "(array([6. , 3.4, 4.5, 1.6]),)\n",
      "(array([5.9, 3.2, 4.8, 1.8]),)\n",
      "(array([6.6, 3. , 4.4, 1.4]),)\n",
      "(array([5.6, 3. , 4.5, 1.5]),)\n",
      "(array([5.8, 2.7, 3.9, 1.2]),)\n",
      "(array([4.9, 2.4, 3.3, 1. ]),)\n",
      "(array([5.9, 3. , 4.2, 1.5]),)\n",
      "(array([6. , 2.9, 4.5, 1.5]),)\n",
      "(array([5.7, 3. , 4.2, 1.2]),)\n",
      "(array([7. , 3.2, 4.7, 1.4]),)\n",
      "(array([6.3, 2.5, 4.9, 1.5]),)\n",
      "(array([5.5, 2.6, 4.4, 1.2]),)\n",
      "(array([6.1, 2.8, 4. , 1.3]),)\n",
      "(array([5. , 2. , 3.5, 1. ]),)\n",
      "(array([6.3, 2.3, 4.4, 1.3]),)\n",
      "(array([5.5, 2.3, 4. , 1.3]),)\n",
      "(array([5.6, 2.7, 4.2, 1.3]),)\n",
      "(array([5.6, 2.9, 3.6, 1.3]),)\n",
      "(array([5.7, 2.8, 4.5, 1.3]),)\n",
      "(array([6.2, 2.9, 4.3, 1.3]),)\n",
      "(array([6.1, 3. , 4.6, 1.4]),)\n",
      "(array([5.5, 2.4, 3.7, 1. ]),)\n",
      "(array([6.7, 3. , 5. , 1.7]),)\n",
      "(array([5.8, 2.7, 4.1, 1. ]),)\n",
      "(array([6.5, 2.8, 4.6, 1.5]),)\n",
      "(array([6. , 2.2, 4. , 1. ]),)\n",
      "(array([6.9, 3.1, 4.9, 1.5]),)\n",
      "(array([5.6, 3. , 4.1, 1.3]),)\n",
      "(array([6.8, 2.8, 4.8, 1.4]),)\n",
      "(array([5. , 2.3, 3.3, 1. ]),)\n",
      "(array([6.3, 3.3, 4.7, 1.6]),)\n",
      "(array([6.2, 2.2, 4.5, 1.5]),)\n",
      "(array([5.7, 2.6, 3.5, 1. ]),)\n",
      "(array([5.1, 2.5, 3. , 1.1]),)\n",
      "(array([6.3, 2.7, 4.9, 1.8]),)\n",
      "(array([6.7, 2.5, 5.8, 1.8]),)\n",
      "(array([6.2, 3.4, 5.4, 2.3]),)\n",
      "(array([5.8, 2.8, 5.1, 2.4]),)\n",
      "(array([4.9, 2.5, 4.5, 1.7]),)\n",
      "(array([6.7, 3.3, 5.7, 2.1]),)\n",
      "(array([6.3, 2.9, 5.6, 1.8]),)\n",
      "(array([6.9, 3.1, 5.1, 2.3]),)\n",
      "(array([6.4, 3.1, 5.5, 1.8]),)\n",
      "(array([6.1, 3. , 4.9, 1.8]),)\n",
      "(array([6.5, 3. , 5.2, 2. ]),)\n",
      "(array([6.3, 3.4, 5.6, 2.4]),)\n",
      "(array([7.2, 3.2, 6. , 1.8]),)\n",
      "(array([7.7, 3. , 6.1, 2.3]),)\n",
      "(array([6.4, 2.7, 5.3, 1.9]),)\n",
      "(array([7.2, 3.6, 6.1, 2.5]),)\n",
      "(array([6.4, 3.2, 5.3, 2.3]),)\n",
      "(array([6. , 3. , 4.8, 1.8]),)\n",
      "(array([5.8, 2.7, 5.1, 1.9]),)\n",
      "(array([6.7, 3.3, 5.7, 2.5]),)\n",
      "(array([6.5, 3. , 5.5, 1.8]),)\n",
      "(array([5.7, 2.5, 5. , 2. ]),)\n",
      "(array([5.9, 3. , 5.1, 1.8]),)\n",
      "(array([6.4, 2.8, 5.6, 2.2]),)\n",
      "(array([7.7, 2.6, 6.9, 2.3]),)\n",
      "(array([6.3, 2.5, 5. , 1.9]),)\n",
      "(array([6.8, 3.2, 5.9, 2.3]),)\n",
      "(array([6.5, 3.2, 5.1, 2. ]),)\n",
      "(array([6. , 2.2, 5. , 1.5]),)\n",
      "(array([7.7, 2.8, 6.7, 2. ]),)\n",
      "(array([6.1, 2.6, 5.6, 1.4]),)\n",
      "(array([6.9, 3.1, 5.4, 2.1]),)\n",
      "(array([6.7, 3. , 5.2, 2.3]),)\n",
      "(array([6.2, 2.8, 4.8, 1.8]),)\n",
      "(array([7.2, 3. , 5.8, 1.6]),)\n",
      "(array([6.9, 3.2, 5.7, 2.3]),)\n",
      "(array([7.6, 3. , 6.6, 2.1]),)\n",
      "(array([5.6, 2.8, 4.9, 2. ]),)\n",
      "(array([6.3, 3.3, 6. , 2.5]),)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'gaussianNB train done!'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print(model.predict([4.4,  3.2,  1.3,  0.2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9. 优缺点\n",
    "优点\n",
    "1. 朴素贝叶斯模型有稳定的分类效率。\n",
    "2. 对小规模的数据表现很好，能处理多分类任务，适合增量式训练，尤其是数据量超出内存时，可以一批批的去增量训练。\n",
    "3. 对缺失数据不太敏感，算法也比较简单，常用于文本分类。\n",
    "\n",
    "缺点:\n",
    "1. 理论上，朴素贝叶斯模型与其他分类方法相比具有最小的误差率。但是实际上并非总是如此，这是因为朴素贝叶斯模型给定输出类别的情况下,假设属性之间相互独立，这个假设在实际应用中往往是不成立的，在属性个数比较多或者属性之间相关性较大时，分类效果不好。而在属性相关性较小时，朴素贝叶斯性能最为良好。对于这一点，有半朴素贝叶斯之类的算法通过考虑部分关联性适度改进。\n",
    "2. 需要知道先验概率，且先验概率很多时候取决于假设，假设的模型可以有很多种，因此在某些时候会由于假设的先验模型的原因导致预测效果不佳。\n",
    "3. 由于我们是通过先验和数据来决定后验的概率从而决定分类，所以分类决策存在一定的错误率。\n",
    "4. 对输入数据的表达形式很敏感。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 10. 参考文献\n",
    "西瓜书\n",
    "https://samanthachen.github.io/2016/08/05/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0_%E5%91%A8%E5%BF%97%E5%8D%8E_%E7%AC%94%E8%AE%B07/\n",
    "\n",
    "https://www.jianshu.com/p/f1d3906e4a3e\n",
    "\n",
    "https://zhuanlan.zhihu.com/p/66117273\n",
    "\n",
    "https://zhuanlan.zhihu.com/p/39780650\n",
    "\n",
    "https://blog.csdn.net/zrh_CSDN/article/details/81007851"
   ]
  }
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